Diffusion, convection, and chemical reaction
Input(s)
\(\boldsymbol{k}_{\mathbf{1}}\): Homogeneous Chemical Reaction Rate Coefficient (1/s)
\(\boldsymbol{D}_{\boldsymbol{A} \boldsymbol{B}}\): Diffusivity \(\left(\mathrm{cm}^{2} / \mathrm{s}\right)\)
\(v_{\boldsymbol{o}}\): Velocity \((\mathrm{cm} / \mathrm{s})\)
\(\boldsymbol{c}_{\boldsymbol{A} \boldsymbol{o}}\): Fraction of Initial Concentration (dimensionless)
z: Vertical Distance \((\mathrm{cm})\)
Output(s)
\(\boldsymbol{c}_{\boldsymbol{A}}\): Fraction of Initial Concentration remaining (dimensionless)
Formula(s)
\[
\mathrm{c}_{\mathrm{A}}=\left(\mathrm{c}_{\mathrm{AO}}\right) * \exp \left(-\left(\left(1+\frac{4 * \mathrm{k}_{1} * \mathrm{D}_{\mathrm{AB}}}{\mathrm{v}_{\mathrm{o}}^{2}}\right)^{0.5}\right)-1\right) *\left(\frac{\mathrm{v}_{\mathrm{o}} * \mathrm{z}}{2 * \mathrm{D}_{\mathrm{AB}}}\right)
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 19, Page: 586.